IndisputableMonolith.Physics.NonlinearDynamicsFromRS
The module NonlinearDynamicsFromRS certifies that Recognition Science forces period-doubling cascades to reach exactly the eight-tick octave. Modelers of chaotic maps or bifurcation sequences cite it to anchor their dynamics in the RS forcing chain rather than ad-hoc parameters. The module supplies type definitions and a certificate object but contains no proofs.
claimPeriod-doubling reaches the eight-tick level: $2^3=8$. The module defines BifurcationType, periodDoublingTarget_8, equilibrium, and NonlinearDynamicsCert as the structures that witness this threshold in systems governed by the Recognition Composition Law.
background
The module imports IndisputableMonolith.Cost, which supplies the J-cost functional and the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. It introduces BifurcationType to classify nonlinear behaviors, periodDoublingTarget_8 to mark the $2^3$ threshold, and NonlinearDynamicsCert as the witness object. The local setting is the extraction of classical nonlinear dynamics from the phi-ladder and the eight-tick octave (T7) of the UnifiedForcingChain.
proof idea
This is a definition module, no proofs. It assembles sibling declarations (BifurcationType, periodDoublingTarget, periodDoublingTarget_8, equilibrium, NonlinearDynamicsCert) that together encode the period-doubling target at the eight-tick level.
why it matters in Recognition Science
The module realizes T7 of the forcing chain (eight-tick octave, period $2^3$) inside the physics layer. It supplies the concrete objects that downstream results in the Recognition framework will use to derive classical nonlinear phenomena from the single functional equation. The doc-comment states the target directly: Period-doubling reaches $2^3=8$.
scope and limits
- Does not contain numerical simulations or explicit bifurcation diagrams.
- Does not prove convergence of the period-doubling cascade beyond the 8-tick mark.
- Does not link the certificate to specific physical systems or experimental data.
- Does not derive the Feigenbaum constant or scaling exponents.